Electric heating appliances, such as toasters, are well known in contemporary households and in commercial settings such as restaurants. Electric heating appliances include electric heating elements, and excessive heating of electric heating elements is undesirable. Thus, it is desirable to establish a design limit on the average operating power supplied to the heating appliance over a pre-defined period of time, and to maintain the actual average operating power during the period of time below the design limit, so as to avoid excessive heating.
The Underwriters' Laboratory, in standard UL-197 section 48, proposes three (3) hour Input Averaging Current (Iavg) as a suitable metric for the design limit and for the actual total operating power. Iavg can be determined according to the equation
                                          I            avg                    =                                                                      I                  1                                ×                                  T                  1                                            +                                                I                  2                                ×                                  T                  2                                            +                              …                ⁢                                                                  ⁢                                  I                  n                                ×                                  T                  n                                                                    T              cyc                                      ;                              T            cyc                    =                                    ∑                              i                =                                  1                  ⁢                                                                          ⁢                  …                  ⁢                                                                          ⁢                  n                                                      ⁢                          T              i                                                          (                  Eqn          .                                          ⁢          1                )            where I1 represents an input current provided to the heating appliance during a first time segment of length T1, In, represents an input current provided to the heating appliance during an nth time segment of length Tn, and Tcyc is the total time period during which the input current is averaged.
UL-197 section 48 further requires that, for a three (3) hour averaging time period Tcyc, the input averaging current Iavg should not exceed eighty percent (80%) of the plug-rated current Irated. Typically, the plug-rated current Irated is a design value that equals or exceeds the full power current IFP through the plug with the heating appliance fully energized.
Various means are known in the art for achieving compliance with UL-197 section 48. For example, existing temperature-limiting circuits have been adapted to limit Iavg based on empirical or calculated correlations between heating element temperatures and Iavg. However, adaptations of temperature-limiting circuits provide only approximate values of the input averaging current Iavg.
Accordingly, it is desirable to have a precise means for determining the input averaging current Iavg by direct electrical measurements in order to achieve compliance with UL standard 197 section 48.